I can't figure out who the father of my unborn child is?!

I had unprotected sex with somebody so ill call him "x" on october 31st. I came home to my fiance that same night an we have sex on a daily basis. I found out I was pregnant december 31st the hospital said I was 6 weeks. What are the chances that X could be the father of my unborn child? Is there even a chance? And I'm pretty sure they can do dna tests before the baby is born would I have to pay for that out of pocket?

Did you expect your period then? You can have bleeding if you are pregnant but it usually doesn't appear like a "normal" period.

Your last period before that would have started around October 26 or so, right? So you had sex on day 5 of your cycle. It's unlikely that you'd get pregnant having sex that early. Usually you'd ovulate between about days 11 and 16 of your cycle and sperm can survive about 5 days.

I did just figure out that there was a 3 week difference between sex with X and the "consieving" date. And I did notice that I had a period my birthday and I bled again on the 25 of dec for a day. Not even. And I haven't bled sense then. An could that make a difference? An could the hospital be wrong on a blood screen and an ultra sound? An how often? Not only that but the obgyn said I was 7 weeks a week after I went to the hospital

There is no way for a doctor, anyone, to know exactly when you conceived. It's all an estimate and usually based on your LMP. They should not be off by "weeks" however, not with an ultrasound.

In October:
Your period should have started around Oct 26. Day 1 of your cycle.
You'd ovulate between Nov 6 and Nov 11. Beginning around Nov 1 there would be a possibility of pregnancy as sperm can survive for about 5 days.
The egg is only viable for about 48 hours. After Nov 13 it is unlikely you'd get pregnant.

In November:
You said you had period on Nov 23. That would be day 1 of your cycle.
You'd ovulate between Dec 4 and Dec 9. Days 11-16 of your cycle. Sperm can survive about 5 days so beginning Nov 29 there is a possibility of pregnancy.
The egg is only viable for about 48 hours. After Dec 11 it is unlikely you'd get pregnant.
Your next period would start around Dec 21.
You can have some bleeding if you are pregnant.

Most doctors base dates on your last menstrual period, November 23. I'd consider November 19 to be "close enough." That means you'd likely conceive around November 30-Dec 5.

You don't have a period if you are pregnant but there can be bleeding. It should not look like a "normal" period. To have a 4 day bleed in November I think it likely it was a period. Your December, one day bleed, would be typical of being pregnant.

I think your fiancee is the father. Yes, DNA tests can be done before birth. Please use a non-invasive method as it has less risk for the baby. They only draw your blood instead of a sample of amniotic fluid.